Computational Fluid Dynamics 2011 Part 14 docx

Computational Fluid Dynamics 384 6.4 Tip-vortex trajectory The tip vortex trajectory was predicted and compared with the experiment measurements. An approximate approach to locate the tip vortex core location is to limit the search for a minimum pressure within the region of the known vortex indicated by a swirl parameter. The physical interpretation for this criterion is given by Jeong and Hussain (Jeong & Hussain, 1995). Within the vortex core, pressure tends to have a local minimum on the axis of a circulatory or swirling motion when the centrifugal force is balanced by the pressure force, which is strictly true only in a steady inviscid planar flow. Using this method, the tip- vortex trajectories were identified from computed flows at the advance ratio of J=1.1. Fig. 8 compared the predicated radial locations of the tip vortex with the experimental observation. In the experiment, the tip vortex was tracked from the blade tip to an axial location of approximately one diameter downstream where x/R=2.0. The current simulation conducted in this study can predict the tip vortex radial trajectory accurately up to a limited distance downstream, due to the grid coarsening in the downstream of the propeller. As shown in Fig. 8, the predicted tip-vortex trajectory is tracked to the location about only one radius downstream at x/R=1.0 before dissipated into the flow field. The largest disagreement between the prediction and the experiment measurement occurs at the last station of x/R=1.0. Beyond that point it appeared to be difficult to trace the tip vortex as it has completely smeared out in the flow field. Examination of the grid resolution of the propeller indicated a finer grid resolution only coving a limited distance in the downstream of the propeller. The grid cells became very coarser as moving beyond the shaft rear surface at station x/R=0.69. Fig. 9 clearly demonstrated the tip vortex convection which is quickly dissipated due to the limited grid resolution. As discussed in the previous section, a refined computational mesh and a higher-order discretization scheme may reduce the numerical dissipation of this vortical flow, although the computational costs would be significantly higher. Fig. 8. Propeller 5168 Tip Vortex Radial Trajectory A Preconditioned Arbitrary Mach Number Scheme Applied to Rotating Machinery 385 Fig. 9. Computed Tip Vortex Visualized by Swirl Parameter 6.5 Tip vortex convection and decay Another way to trace the tip vortex of the propeller is to use a non-dimensional parameter termed intrinsic swirl parameter τ (Berdahl & Thompson, 1993), which calculates the velocity gradient tensor over the computational domain. The intrinsic swirl indicates the tendency for the fluid to swirl about a local point, and is more effective to represent the vortical motion in the flow field. In regions where the swirl parameter approaches to zero ( 0 τ → ), the fluid convects too rapidly to be captured in swirling motion, while in region where 0 τ > , the fluid does not move quickly enough and is trapped in a swirling motion. Fig. 10 compares the tip vortex strength under the four advance coefficients. The intrinsic swirl contours are visualized on six downstream stations of x/R=[0.1, 0.6] with an equal spacing of 0.1. Streamlines are generated from the shaft rear surface at x/R=0.69. The core regions of blade tip vortices are evident by the largest magnitude of swirl parameter. It clearly shows the rapid decay of the tip vortices and the separation of vortices from the wake as the flow moves downstream. The swirl parameter values at the vortex core on selected stream-wise stations are extracted and presented in Fig. 11. The simulation results indicated that vortex strength varied strongly with advance coefficient. At a high loading (lower advance ratio values, J=0.98 and 1.10), strong tip vortices are observed over a longer distance downstream. The tip vortices are very weak at J=1.27 and eventually disappeared at J=1.51. It is noticed that the decreasing of the intrinsic swirl under the advance coefficients of J=1.27 and 1.51 is not monotonic as x/R goes beyond 0.4, where the swirl parameter even increases at further downstream stations. Further investigation found that the locations of high swirl centers at station x/R=0.5, 0.6 under J=1.27 and 1.51 occur in a much finer grid region, which was originally generated for the purpose of capturing the propeller wake. Therefore, the non-physical behaves of the swirl parameter appear in Fig. 11 are due to the variation of grid resolution. The simulation results are qualitatively consistent with the experimental measurements. Computational Fluid Dynamics 386 Fig. 10. Predicted Wakes and Tip Vortices vs. Advance Coefficient A Preconditioned Arbitrary Mach Number Scheme Applied to Rotating Machinery 387 Fig. 11. Tip Vortex Decay vs. Advance Coefficient J 6.6 Tip-vortex attachment The water tunnel experiment also observed suction-side tip vortex attachment occurred aft of the blade tip over certain range of tested advance ratio. The locations of the tip vortex attachment on the five blades showed minor variation from blade to blade, and their average radial location has been estimated. In the open-water experiment at an advance ratio of J=0.98, this average location was estimated at the blade trailing edge of 0.99R radius, while at J=1.1, the attachment point was moved aft to 0.998R radius of the trailing edge. From the current computed results, the iso-surface of swirl parameter τ=1.0 is generated to visualize the tip vortex structure as shown in Fig. 12. The iso-surface is shaded by static Fig. 12. Blade Suction Side Tip Vortex Attachment. Computational Fluid Dynamics 388 pressure. The propeller geometry is not plotted in the figure, but the tip region of the propeller blade is seen clearly, which is actually the swirl iso-surface in the blade boundary layer. At the blade tip, the attachment occurs aft a local minimum pressure center at the trailing edge. The iso-surface of the swirl parameter indicated that the tip vortex attachment occurs at the trail edge on the blade suction side between 0.994R-0.999R. The variation of the attachment points at J=0.98 and J=1.1 are not distinguishable except that the local minimum pressure center upstream the attachment location has lower pressure at J=0.98 and originates stronger tip vortex. The current simulations correctly captured the tip-vortex attachment observed in the experiment, which is important for the improved understanding of the cavitation inception of the marine propeller. 7. Conclusion A modified preconditioning method was investigated and validated in the prediction of hydrodynamic viscous flows for marine propeller P5168. The preconditioning parameter is based on the reference Mach number and rotating Mach number to provide stable and accurate solutions for low Mach number flows in rotating machinery, while the original preconditioning method failed to provide converged solutions in the case presented in this study. The predicted overall propeller performance, circumferentially averaged velocities, mean velocity contours, tip-vortex trajectory and decay at blade downstream stations are validated against the experimental data. The comparison between the computation and the experiment indicates that the current preconditioned solver was able to capture the general features of the tip vortex generated by the propeller. In particular, the predicted thrust and torque coefficients at several advance ratios matched well with the open-water experimental data. However, the current numerical simulation showed a quick decay of the tip vortex in the propeller downstream, due to a lack of enough grid resolution. Future studies include using adaptive grid technique to locally refine the computational mesh in the vortex core region, and a higher-order spatial discretization schemes to further reduce the numerical diffusion in the solver. 8. Acknowledgements The author wishes to thank Qiuying Zhao of The University of Toledo and Xiao Wang of High Performance Computing Collaboratory at Mississippi State University for helping processing the simulation data and formatting the manuscript. 9. References Anderson, W.K. (1992). Grid Generation and Flow Solution Method for Euler Equations on Unstructured Grids, NASA Technical Report TM– 4295, April 1992. Anderson, W.K.; Rausch, R.D., & Bonhaus, D. L. (1995). Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids, AIAA Paper 95–1740, June 1995. Berdahl, C. H. and Thompson, D. S., (1993). Eduction of Swirling Structure using the Velocity Gradient Tensor, AIAA J., vol. 31, no. 1, (January 1993), 97-103. A Preconditioned Arbitrary Mach Number Scheme Applied to Rotating Machinery 389 Briley, W.R., and McDonald, H., and Shamroth, S.J., (1983). A Low Mach Number Euler Formulation and Application to Time Iterative LBI Schemes, AIAA J., 21 (10), (1983),1467–1469. Briley, W.R., Tayler, L.K., and Whitfield, D.L., (2003). High–Resolution Viscous Flow Simulations at Arbitrary Mach Number, Journal of Computational Physics, 184(1), (2003), 79-105. Chesnakas, C.J., and Jessup, S.D., (1998). Cavitation and 3–D LDV Tip–Flowfield Measurements of Propeller 5168, CRDKNSWC/HD–1460–02, (May 1998), Carderock Division, Naval Surface Warfare Center. Chen, J.P.; Ghosh, A.R., Sreenivas, D., & Whitfield, D.L. (1997). Comparison of Computations Using Navier–Stokes Equations in Rotating and Fixed Coordinates for Flow Through Turbomachinery, AIAA Paper No.97–0878, AIAA 35th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 6–10, 1997. Choi, D., & Merkle, C.L. (1985). Application of Time–Iterative Schemes to Incompressible Flow, AIAA J., 23 (10):1518–1524, 1985. Choi, D., & Merkle, C.L. (1993). Application of Preconditioning to Viscous Flows, J. Comp. Physics, 105:207–223, 1993. Chorin, A.J. (1967). A Numerical Method for Solving Incompressible Viscous Flow Problems, J. Comp. Physics, 2:12–26, 1967. Coirier, W.J. (1994). An Adaptively–Refined, Cartesian, Cell–Based Scheme for the Euler and Navier–Stokes Equations, NASA Technical Memorandum 106754, NASA Lewis Research Center, October 1994. Hyams, D.G. (2000), An Investigation of Parallel Implicit Solution Algorithms for Incompressible Flows on Unstructured Topologies, Ph.D. Dissertation, Mississippi State University, May 2000. Hageman, L.A. and Young, D.M., (1981). Applied Iterative Methods, 1981, Academic Press, New York. Jeong, J. and Hussain, F., (1995). On the Indentification of a Vortex, Journal of Fluid Mechanics, Vol. 285, (1995), 69-94. Marcum, D. L., (2001). Efficient Generation of High Quality Unstructured Surface and Volume Grids, Engineering with Computers, Vol. 17, No. 3, (2001), 211-233. O’Brien, G.G., Hyman, M.A., and Kaplan, S., (1951), A Study of the Numerical Solution of Partial Differential Equations, Journal of Mathematics and Physics, Vol 29, No. 4, (1951), 223-249. Sheng, C., and Wang, X., (2006). A Global Preconditioning Method for Low Mach Number Viscous Flows in Rotating Machinery, GT2006-91189, Proceedings of ASME Turbo Expo 2006, 8-11 May 2006, Barcelona, Spain. Sheng, C., and Wang, X., (2003). Characteristic Variable Boundary Conditions for Arbitrary Mach Number Algorithm in Rotating Frame, AIAA-2003-3976, Proceedings of the 16th AIAA Computational Fluid Dynamics Conference, June 23-26, 2003, Orlando, FL. Sheng, C. and Wang, X., (2009). Aerodynamic Analysis of a Spinning Missile with Dithering Canards Using a High Order Unstructured Grid Scheme, AIAA-2009-1090, 47th AIAA Aerospace Sciences Meeting, 5-8 January 2009, Orlando, Florida. Computational Fluid Dynamics 390 Spalart, P., and Allmaras, S., (1991). A One-Equation Turbulence Model for Aerodynamic Flows, AIAA Paper 92-0439, January 1991. Vichnevetsky, R., and Bowles, J.B., (1982). Fourier Analysis of Numerical Approximations of Hyperbolic Equations, 1982. Wang, X. and Sheng, C., (2005). Numerical Study of Preconditioned Algorithm for Rotational Flows, 17th AIAA Computational Fluid Dynamics Conference, June 6–9, 2005, Toronto, Ontario, Canada Wang, X., (2005). A Preconditioned Algorithm for Turbomachinery Viscous Flow Simulation. Ph.D. Dissertation, Mississippi State University, December 2005. 17 Modelling Hydrodynamic Drag in Swimming using Computational Fluid Dynamics Daniel A. Marinho 1,2 , Tiago M. Barbosa 2,3 , Per L. Kjendlie 4 , Narendra Mantripragada 2,5 , João P. Vilas-Boas 6,7 , Leandro Machado 6,7 , Francisco B. Alves 8 , Abel I. Rouboa 9,10 and António J. Silva 2,11 1 University of Beira Interior. Department of Sport Sciences (UBI, Covilhã) 2 Research Centre in Sports, Health and Human Development (CIDESD, Vila Real) 3 Polytechnic Institute of Bragança. Department of Sport Sciences (IPB, Bragança) 4 Norwegian School of Sport Sciences. Department of Physical Performance (Oslo) 5 IIT Kharagpur. Department of Aerospace Engineering (Mumbai) 6 University of Porto, Faculty of Sport (FADEUP, Porto) 7 Centre of Research, Education, Innovation and Intervention in Sports (CIFI2D, Porto) 8 Technical University of Lisbon. Faculty of Human Kinetics (FMH-UTL, Lisbon) 9 University of Trás-os-Montes and Alto Douro. Department of Engineering (UTAD, Vila Real) 10 Research Centre and Technologies of Agro-environment and Biological Sciences (CITAB, Vila Real) 11 University of Trás-os-Montes and Alto Douro. Department of Sport Sciences, Exercise and Health (UTAD, Vila Real) 1,2,3,6,7,8,9,10,11 Portugal 4 Norway 5 India 1. Introduction In the sports field, numerical simulation techniques have been shown to provide useful information about performance and to play an important role as a complementary tool to physical experiments. Indeed, this methodology has produced significant improvements in equipment design and technique prescription in different sports (Kellar et al., 1999; Pallis et al., 2000; Dabnichki & Avital, 2006). In swimming, this methodology has been applied in order to better understand swimming performance. Thus, the numerical techniques have been addressed to study the propulsive forces generated by the propelling segments (Rouboa et al., 2006; Marinho et al., 2009a) and the hydrodynamic drag forces resisting forward motion (Silva et al., 2008; Marinho et al., 2009b). Although the swimmer’s performance is dependent on both drag and propulsive forces, within this chapter the focus is only on the analysis of the hydrodynamic drag. Therefore, this chapter covers topics in swimming drag simulation from a computational fluid dynamics (CFD) perspective. This perspective means emphasis on the fluid mechanics and Computational Fluid Dynamics 392 CFD methodology applied in swimming research. One of the main aims for performance (velocity) enhancement of swimming is to minimize drag forces resisting forward motion, for a given trust. This chapter will concentrate on numerical simulation results, considering the scientific simulation point-of-view, for this practical implication in swimming. In the first part of the chapter, we introduce the issue, the main aims of the chapter and a brief explanation of the CFD methodology. Then, the contribution of different studies for swimming using CFD and some practical applications of this methodology are presented. During the chapter the authors will attempt to present the CFD data and to address some practical concerns to swimmers and coaches, comparing as well the numerical data with other experimental data available in the literature. 2. Fluid mechanics and CFD methodology 2.1 Background CFD is a branch of fluid mechanics that solves and analyses problems involving a fluid flow with computer-based simulations. CFD methodology consists of a mathematical model that replaces the Navier-Stokes equations with discretized algebraic expressions that can be solved by iterative computerized calculations. The Navier–Stokes equations describe the motion of viscous non-compressible fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the fluid stress is the sum of a diffusing viscous term (proportional to the gradient of velocity), plus a pressure term. A solution of the Navier–Stokes equations is called a velocity field or flow field, which is a description of the velocity of the fluid at a given point in space and time. CFD methodology is based on the finite volume approach. In this approach, the equations are integrated over each control volume. It is required to discretize the spatial domain into small cells to form a volume mesh or grid, and then apply a suitable algorithm to solve the equations of motion. In addition, CFD analyses complements testing and experimentation, reducing the total effort required in the experimental design and data acquisition. In the early days of its application, CFD was quite difficult to use. It was only applied by a few high technological level companies, in the Aerospatiale Engineering or in some specific scientific research areas. It became obvious that its application had to assume a user friendly interface and to progress from a heavy and difficult computation to practical, flexible, intuitive and quick software. Therefore, the following step was to transform CFD in a new set of commercial software to be used in different applications and to improve the user interface. Presently, this tool is used in the solution of complex engineering problems involving fluid dynamics and it is also being extended to the study of complex flow regimes that define the forces generated by animal species in self propulsion. The basic steps of CFD analysis are: 1. Problem identification and pre-processing: (i) define the modelling goals, (ii) identify the domain to model, (iii) design and create the grid. 2. Solver execution: (i) set up the numerical model, (ii) compute and monitor the solution. 3. Post-Processing: (i) examine the results; (ii) consider revisions to the model. 2.2 Advantages and limitations CFD can be used to predict fluid flow, heat and mass transfer, chemical reactions and related phenomena by solving the set of governing mathematical equations. The results of [...]... Kellar, W.P.; Pearse, S.R.G & Savill, A.M (1999) Formula 1 car wheel aerodynamics Sports Engineering, 2, 203-212 Liu, H (2002) Computational biological fluid dynamics: digitizing and visualizing animal swimming and flying Integrative and Comparative Biology, 42, 1050-1059 Lyttle, A & Keys, M (2006) The application of computational fluid dynamics for technique prescription in underwater kicking Portuguese... velocities of particles in fluidized or settling beds vr , s is the terminal velocity correlation for the solid phase (Garside and AlDibouni, 1977): ( 4 .14 vr , s = 0.5 α w − 0.06Re s + ( 0.06 Re s ) 2 2.65 4 .14 8.28 + 0.12 Re s ( 2α w − α w ) + α w ) (14) Lift forces act on a particle mainly due to velocity gradients in the primary-phase flow field The lift force will be more significant for larger particles... shear stress on the wall of the carotid artery using magnetic resonance imaging and computational fluid dynamics Studies in Health Technology and Informatics, 113, 412-442 Zaidi, H.; Taiar, R.; Fohanno, S & Polidori, G (2008) Analysis of the effect of swimmer’s head position on swimming performance using computational fluid dynamics Journal of Biomechanics, 41, 1350-1358 18 Hydrodynamic Behavior of Flow... K sw ( = K ws ) is the interphase momentum exchange coefficient The fluid- solid exchange coefficient K sw can be written in the following general form: K sw = α s ρs f τs (9) where τ s , the particulate relaxation time, is defined as τs = ρs ds2 18 μ w where ds is the diameter of particles of phase s (10) 408 Computational Fluid Dynamics For the Syamlal-O'Brien model (1989), f = C D Re s α w 24 vr2,... swimming Medicine and Science in Sports and Exercise, 23, 6, 744-747 Bixler, B & Schloder, M (1996) Computational fluid dynamics: an analytical tool for the 21st century swimming scientist Journal of Swimming Research, 11, 4-22 Bixler, B.; Pease, D & Fairhurst, F (2007) The accuracy of computational fluid dynamics analysis of the passive drag of a male swimmer Sports Biomechanics, 6, 81-98 Chatard, J.C... was supported by the Portuguese Government by Grants of the Science and Technology Foundation (PTDC/DES/098532/2008) 402 Computational Fluid Dynamics 7 References Barsky, S.; Delgado-Buscalioni, R & Coveney, P.V (2004) Comparison of molecular dynamics with hybrid continuum-molecular dynamics for a single tethered polymer in a solvent Journal of Chemical Physics, 121, 2403-2411 Bassett, D.R.; Flohr, J.;... at the bottom of the clarifier, and a dynamic upward particles’ surface Compared with figures 5a to 5c, it is obviously shown that as time passes, the 410 Computational Fluid Dynamics particles boundary becomes higher (white dash line), i.e., many particles rise and the loading of the following fast filtration becomes heavy In order to enunciate the geometric effects on the stability of the sludge blanket,... Water Res., 25, 1263 (1991) Tao, T., X F Peng, A Su, D J Lee, “Modeling Convective Drying of Wet Cake,” J Chin Inst Chem Eng., 39, 287 (2008) 412 Computational Fluid Dynamics Videla, A R., C L Lin, and J D Miller, “Simulation of Saturated Fluid Flow in Packed Particle Beds-The Lattice-Boltzmann Method for the Calculation of Permeability from XMT Images,” J Chin Inst Chem Eng., 39, 117 (2008) Weiss, M.,... and experimental data on tethered DNA in flow Moreover, Gage et al (2002) reported that computational techniques coupled with experimental verification can offer insight into model validity and showed promise for the development of accurate three-dimensional simulations of medical procedures 394 Computational Fluid Dynamics In engineering one can cite, for example, Venetsanos et al (2003) illustrated... larger particles Thus, the inclusion of lift forces is not appropriate for closely packed particles or for very small particles When a secondary phase p accelerates relative to the primary phase q, the inertia of the primary phase mass encountered by the accelerating particles exerts a virtual mass force on the particles The virtual mass effect is significant when the secondary pahse density is much . swimming drag simulation from a computational fluid dynamics (CFD) perspective. This perspective means emphasis on the fluid mechanics and Computational Fluid Dynamics 392 CFD methodology. (PTDC/DES/098532/2008). Computational Fluid Dynamics 402 7. References Barsky, S.; Delgado-Buscalioni, R. & Coveney, P.V. (2004). Comparison of molecular dynamics with hybrid continuum-molecular dynamics. & Savill, A.M. (1999). Formula 1 car wheel aerodynamics. Sports Engineering, 2, 203-212. Liu, H. (2002). Computational biological fluid dynamics: digitizing and visualizing animal swimming